IN connexion with photometric determination of specific surface of finely divided material, it is essential to know the relation between the projected area of particles, which is actually measured, and the corresponding surface area. The solution of this problem was first given by A. Cauchy in his "Memoire sur la rectification des courbes et la quadrature des surfaces courbes" (Paris, 1832)1. A short account of his results in the form of theorems was later published in the Comptes rendus2, but no formal proof was given. It is the latter paper which is usually referred to in connexion with the above problem.